Urgent Center of mass and relevant stuffs

A vertical spring of constant k is attached at the bottom to a platform of mass mp, and at the top to a massless cup. The platform rests on a scale. A ball of mass mb is placed in the cup. What is the reading on the sacle when (a) the spring is compressed an amount d= mb*g/k (b) the ball comes to rest momentarily with the spring compressed ? (c) the ball again comes to rest in its original position ??

I'm stumbling through the same problem myself. This is what I've managed to come up with to (a), I haven't solved (b) or (c) yet. I'm new to this site (obviously) and I think that underscores are used to indicate subscript and carets are used to indicate superscript, yes? That's what I've used here, in any case.

I think that a_b*m_b = dk, and if so, then a_b*m_b = (m_b*g/k)*k = m_b*g so the final answer would be

F_n = g(m_b + m_p) + a_b*m_b

I know you're not supposed to just solve the OP's answer for them, but I have no idea if I've gotten this right, and I don't know how to do (b) and (c) (although I think that (c) is just F_n = g(m_b + m_p) but I'm not sure and it seems too easy). I'm not solving it for them intentionally; I'm just hijacking the thread to ask for help on the same question, and since the OP didn't show any work, I thought perhaps it'd be helpful if I showed mine.